How Does Mass Affect Calculations in Non-conservative Force Problems?

[kristen151027]

I'm having trouble with the following problem:

"There is a car ready to go down a hill. The height of the hill is 9.0 m, and the length of the slope is 11.0 m (hypotenuse). The frictional force opposing the car is 125 N, and the car must be going 12.5 m/s when it reaches the bottom. What is the initial speed required for the car to overcome friction and reach required speed at the bottom of the hill?"

I set up the following equation: KE_i + PE_i + (frictional force)(cos 180)(11.0 m) = KE_f

I don't know if I have the right setup because whenever I try to solve it, I run into trouble because there is no mass provided and I get an answer to be around 50 (it should be a little less than 3 m/s).

 

[Päällikkö]

You can express the frictional force in terms of the normal force. Mass will thus cancel out.

 

[HallsofIvy]

cos 180?? That's equal to -1 but why do you have that? There is no 180 angle in your problem. If you want the cosine of the angle the hill makes, then you can use the Pythagorean theorem to get the "near side".

 

[kristen151027]

By using the pythagorean theorem and the law of sines, I found the normal force to be approx. 5.17 N, which I multiplied by 11.0 m to get 56.92 J. Correct? Then I inserted that in the equation:

KE_i + PE_i + (normal force x hypotenuse) = KE_f

But I got the wrong answer. What am I doing wrong?

 

[Doc Al]

I set up the following equation: KE_i + PE_i + (frictional force)(cos 180)(11.0 m) = KE_f

I see nothing wrong with this equation or your approach. (The "cos 180" may look strange, but it is correct since the friction force and displacement are 180 degrees apart.)

However I don't see how you can solve the problem without additional information, such as the mass of the car.